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Write an equation to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term. \newline–1, 4, –16, …–1,\,4,\,–16,\,\dots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____)n−1\left(\_\_\_\_\right)^{n - 1}

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Q. Write an equation to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term. \newline–1, 4, –16, …–1,\,4,\,–16,\,\dots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____)n−1\left(\_\_\_\_\right)^{n - 1}
  1. Identify Pattern: Identify the pattern in the sequence.\newlineThe given sequence is −1,4,−16,…-1, 4, -16, \ldots\newlineWe notice that each term changes sign and is multiplied by a common ratio.\newlineThis indicates that the sequence is geometric with alternating signs.
  2. Determine Terms: Determine the first term a1a_{1} and the common ratio rr. The first term is a1=−1a_{1} = -1. To find the common ratio, we divide the second term by the first term: r=4(−1)=−4r = \frac{4}{(-1)} = -4.
  3. Write Formula: Write the general formula for the nnth term of a geometric sequence.\newlineThe nnth term of a geometric sequence is given by an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n - 1)}.
  4. Substitute Values: Substitute the values of a1a_1 and rr into the formula.\newlineWe have a1=−1a_1 = -1 and r=−4r = -4.\newlineSo, the formula for the nth term is an=(−1)×(−4)(n−1)a_n = (-1) \times (-4)^{(n - 1)}.

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